House Democratic leaders have cleared the way for an amendment to cut $500 million from the Democratic welfare bill in an effort to win support for the measure from wavering Democratic fiscal conservatives and moderates.

House Speaker Jim Wright (D-Tex.) said yesterday that floor debate, which was to have started yesterday, had been postponed until Tuesday. The outlook for passage of the bill had been considered uncertain because of strong opposition from the Reagan administration and conservatives to provisions in the Democratic bill.

Wright said that before the proposed amendment was drafted and permitted Wednesday night by the Rules Committee, he had doubted that a resolution governing floor debate and allowing only one floor amendment, a Republican substitute, could pass.

As drafted by the Ways and Means Committee, the Democratic bill focuses on training programs to help welfare mothers get jobs, but it also would enhance some benefits. It would cost $5.5 billion over five years, plus about $600 million for changes in the food stamp program.

The amendment to cut $500 million from this total will be offered by Rep. Michael A. Andrews (D-Tex.). It was drafted after 79 Democrats signed a letter to Wright complaining that the Rules Committee resolution governing floor debate on the bill did not allow any amendments except the Republican substitute, which would provide $1.1 billion over five years, basically all for training and related programs.

The letter did not discuss money. But many of those who signed it had made clear earlier that they felt that the GOP bill provided too little money, the Democratic bill too much.

Many of the bill's supporters said they feared that unless some amendment were permitted that cut the amount in the Ways and Means bill somewhat, but not as much as the GOP plan, the bill either would be defeated or the House would reject the resolution governing debate, with Democrats like Rep. Thomas Richard Carper (D-Del.) leading the way, and open the bill to added amendments, which also could kill it.

The Andrews amendment would save $500 million over five years by:Requiring all states to automatically deduct child-support payments from the wages of an absent parent, even if not in arrears.

Providing child-care subsidies to welfare mothers for 12 months after they stop receiving welfare benefits, but only if family income is under 150 percent of the poverty line and only if they leave the welfare rolls as a result of earnings from a job. This excludes from the child-care benefits women who work part-time but leave the rolls by getting married.

Providing that enhanced federal reimbursements to states that raise welfare benefits would not apply to any benefit increases that occur after Oct. 1, 1991.

Carper has sought but failed to obtain permission to offer a substitute bill costing $2.4 billion over five years. An aide said yesterday that while Carper views the Andrews amendment as "a positive step," he will still seek to defeat the rule governing debate and open the bill to further amendments. "They've given us an inch and we needed at least a foot," a spokesman said.

Carper and Rep. Thomas J. Downey (D-N.Y.), who is one of the chief sponsors of the Democratic bill, negotiated unsuccessfully toward a compromise for several days.